Iconic Arithmetic Volume I The Design Of Mathematics For Human Understanding William Bricken by William Bricken 9781732485136, 1732485135 instant download after payment.

Over the last two centuries, arithmetic has devolved from physical manipulation of objects to memorization of strings of abstract symbols. Iconic Arithmetic Volume I introduces two innovative types of postsymbolic arithmetic that reunite sensual experience with the formal structure of numbers. Iconic numbers are icons that look and feel like what they mean. This book demonstrates that the universally accepted numbers we currently use are a design choice and not the way that arithmetic must necessarily work.
In ensemble arithmetic adding is putting icons together, multiplying is putting icons inside each other. Neither requires cognitive effort. In James algebra numeric concepts and operations are expressed as different ways of arranging containers. Both systems support a multitude of physical, interactive and multidimensional dialects that are described in the book.
James algebra is based on the iconic logic developed by Charles Sanders Peirce, George Spencer Brown and Louis Kauffman. It reduces the “laws” of arithmetic and algebra to three simple patterns of containment. Two of these patterns delete unnecessary symbolic complexity found in integer, rational, irrational and complex numeric expressions.
The postsymbolic innovations of iconic arithmetic modify the formal structure of mathematics in fundamental and surprising ways:
- Arithmetic needs only one concept, distinction, and one structure, the container.
- Difference is more important than equality.
- Meaning is based on existence rather than on truth or numeric value.
- Zero is self-contradictory; instead the inside of an empty container is void.
- Objects and operations are two sides of the same boundary.
- Numbers, even exponents, do not need a base (e.g. base 10).
- There is only one inverse operation seen from different perspectives.
- Parallel deletion of structure is a more efficient way to compute.